Question

3. Given: y =(x+1)?
Domain
Range
Opening of
the Parabola
Vertex
Axis of
Symmetry
x-intercept
y-intercept
​

Answer 1

Vertex: (−4,26))

Axis of symmetry: x=−4

y-intercept: 10

x-intercepts: −4±√26

Domain: R

Range: R∩(−∞,26]

Explanation:

Vertex

Re-writing y=−x2−8x+10 in vertex form:

XXXy=(−1)(x2+8x+42)+10+16)

XXXy=(−1)(x−(−4))2+(26)

with vertex at (−4,26)

Axis of Symmetry

Any parabola in the form y=ax2+bx+c has as an axis of symmetry the vertical line passing through the vertex.

In this case x=−4

y-intercept

The y-intercept is the value of y when x=0

XXXy=−(0)2−8(0)+10=10

x-intercepts

The x-intercepts are the values of x when y=0

0=(−1)(x+4)2+26

(x+4)2=26

x+4=±√26

x=−4±√26

Domain

y=−x2−8x+10 is defined for all Real values of x

Range

Since a parabolic equation with a negative coefficient for the x2 term opens downward, the vertex gives a maximum value for the Range.

The Range is ≤26

Step-by-step explanation:

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